Multiple object tracking (MOT) is a common task used to investigate limitations on human visual attention. However, the nature of these limitations is still unknown. A priori, there are at least four plausible constraints that could limit performance. First, there could be a fixed upper bound on the number of objects tracked. Second, there may be a limit on sampling speed, a possibility consistent with a hypothesized ‘alternating spotlight’ of attention. Third, there may be limits on memory for the velocity and position of any particular object (a fixed resource determines the precision of memory for the tracked objects). Finally, there may be a limit on the precision of observations, consistent with the hypothesis of a fixed distribution of attentional enhancement which improves sensitivity in particular regions of space. The multiple object tracking task is computationally identical to an “aircraft tracking” problem (finding the correspondence between objects from one time to the next). Therefore to model human performance in MOT, we implemented a probabilistic tracking model and included each of the four constraints described above. Experimental data on MOT show a standard pattern: as the number of objects increases, human tracking performance decreases. Consistent with work by Alvarez & Franconeri (in press), putting a simple limit on the number of objects our model can track does not account for existing patterns of data. However, simulations with limited memory, limited precision, and limited sampling speed all produced a close fit to existing datasets. We describe the probabilistic model we used to conduct these simulations as well as a set of experiments in progress in which we independently vary both the predictability of object motion and the sample rate of object displays.